From the problem statement, it is clear that each of the smaller triangles are of the same area (all are equilateral triangles and the ratio of the sides etc implies this). Since three of the four triangles are shaded, the shaded area of the bigger triangle is K*3/4.
OR (I proceeded the following way a bit before realizing the above
you could solve it by finding the areas of the bigger triangle and the smaller ones and doing a ratio of them.
Let 's' be the side of the bigger triangle. Since this is an equilateral, the area is = s^2 * sqrt(3)/4.
Now for the smaller triangle. we know that the side of smaller triangle is half that of the bigger one. So, area = (s/2)^2 * sqrt(3)/4.
Now substitute K for (s^2) * sqrt(3)/4 in the smaller triangle and subtract this from K to get the answer of 3K/4.
-Neni
